The moving cluster method is one of the methods for determining the distance to a star cluster in astrometry . [1] In the first half of the 20th century, this method was applied to several clusters closest to the Sun. At present, more accurate methods are used to determine the distance to clusters.
Theoretical Background
The moving cluster method is based on observing the proper motion and Doppler shift of each object in the cluster. Since the objects in the cluster are located close to each other (compared with the distance from the observer to the cluster), in the sky they will move towards one point, which is a manifestation of the perspective effect.
The distance d to the cluster star is determined by the formula
where u represents the proper motion of the star, v r is the radial velocity , θ is the angle between the direction of the star and the direction of convergence of the stellar velocity vectors. Further, the values obtained for several stars can be averaged.
Application
The method was used to determine distances only for a small number of clusters. In order for this method to be applicable, it is necessary that the cluster is located close to the Sun, at a distance of no more than several hundred parsecs , and also it should be quite close and stand out well among the background stars. The method is quite laborious compared to the method of trigonometric parallaxes , but gives a less accurate result compared to modern high-precision measurements carried out, for example, by the Hipparcos satellite .
Among the clusters, the distance to which was determined by this method, Hyades and Pleiades can be noted.
Recently, this method was used to determine the distance between the brown dwarf 2M1207 and the exoplanet 2M1207b . In December 2005, the American astronomer Eric Mamajek received a distance value of 2M1207b equal to 53 ± 6 pc . [2]
Notes
- ↑ James Binney, Michael Merrifield. Galactic Astronomy. - Princeton, New Jersey: Princeton University Press, 1998 .-- ISBN 0-691-00402-1 .
- ↑ Mamajek. A Moving Cluster Distance to the Exoplanet 2M1207b in the TW Hydrae Association (Eng.) // The Astrophysical Journal : journal. - IOP Publishing 2005. - Vol. 634 , no. 2 . - P. 1385-1394 . - DOI : 10.1086 / 468181 . - . - arXiv : astro-ph / 0507416 .